Numbers, sets, and axioms : the apparatus of mathematics  pbk.

A.G. Hamilton

Following the success of Logic for Mathematicians, Dr Hamilton has written a text for mathematicians and students of mathematics that contains a description and discussion of the fundamental conceptual and formal apparatus upon which modern pure mathematics relies. The author's intention is to remove some of the mystery that surrounds the foundations of mathematics. He emphasises the intuitive basis of mathematics; the basic notions are numbers and sets and they are considered both informally and formally. The role of axiom systems is part of the discussion but their limitations are pointed out. Formal set theory has its place in the book but Dr Hamilton recognises that this is a part of mathematics and not the basis on which it rests. Throughout, the abstract ideas are liberally illustrated by examples so this account should be well-suited, both specifically as a course text and, more broadly, as background reading. The reader is presumed to have some mathematical experience but no knowledge of mathematical logic is required.

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  • Preface
  • 1. Numbers
  • 2. The size of a set
  • 3. Ordered sets
  • 4. Set theory
  • 5. The axiom of choice
  • 6. Ordinal and cardinal numbers
  • Hints and solutions to selected exercises
  • References
  • Index of symbols
  • Subject index.

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書名 Numbers, sets, and axioms : the apparatus of mathematics
著作者等 Hamilton, A. G.
巻冊次 pbk.
出版元 Cambridge University Press
刊行年月 1982
ページ数 ix, 255 p.
大きさ 24 cm
ISBN 0521287618
NCID BA00984333
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言語 英語
出版国 イギリス